Characterizing Persistent Cycles and Trends of Climate Dynamics with Operator-Theoretic Techniques

In recent years, operator-theoretic techniques have proven to be highly fruitful for analysis of data generated by complex systems. These methods leverage the spectral properties of Koopman and transfer operators (which govern the evolution of observables and probability distributions, respectively, under nonlinear dynamics) to perform mode decomposition, forecasting, and other related tasks. In this presentation, we describe how operator-theoretic approaches, combined with methods from machine learning, identify observables of climate dynamics on subseasonal to decadal timescales with two main features: slow correlation decay and cyclicity. These observables are approximate eigenfunctions of Koopman evolution operators, estimated from time series data from models or observations using kernel methods. Using eigenfunctions computed from Indo-Pacific SST, or multivariate OLR/wind data, we construct indices of the El Nino Southern Oscillation and Madden-Julian oscillation, respectively, with favorable predictability properties. In addition, we show that eigenfunctions of Koopman operators are useful in identifying the decadal climate-change trend over the industrial era, as well as the modulation of the seasonal precipitation cycle by ENSO and the climate-change trend.